Modelling Effects of Wind Fields in Cloth Animations
M. Keckeisen, S. Kimmerle, B. Thomaszewski, and M. Wacker
WSI/GRIS
University of Tübingen
Sand 14,
D-72076 Tübingen, Germany
{keckeisen, kimmerle, wacker}@gris.uni-tuebingen.de
[email protected]
ABSTRACT
In this paper we show how to incorporate effects of wind fields in cloth animations. We discuss two different
approaches to model force fields describing air motion and show how these models can be augmented to exhibit
interaction with deformable thin objects such as textiles. The first model is based on the Navier-Stokes equations,
while the second method extends simple particle tracing methods by the effect of lee. In each case, we present a
method for simulating the interaction of cloth movements with the wind field. Both methods have been integrated
in an existing cloth simulation system, and we compare their respective advantages and disadvantages.
Keywords
Wind Simulation, Cloth Animation, Physically Based Modelling, Computer Graphics.
1. INTRODUCTION
While the simulation of wind is an area of vast interest
in aerodynamic engineering, computational fluid dynamics (CFD), and animation/visualisation of fluids in
computer graphics, it has been a rather abandoned subject in simulation of deformable objects such as cloth
simulation. This is mostly due to the fact that conventional CFD applications require enormous computational power. However, aerodynamic effects are obviously capable of enhancing the realism of an animated scene and thus are an important part of a cloth
simulation system. For example, air resistance is a vital component which cannot be neglected if realistic
animation is desired [BTH + 03].
In this work we discuss two different approaches to
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Journal of WSCG, Vol.12, No.1-3., ISSN 1213-6972
WSCG 2004, February 2-6, 2003, Plzen, Czech Republic.
Copyright UNION Agency – Science Press.
model force fields describing air motion and show how
these forces can be applied to generate aerodynamic
effects on textiles. The first method is based on modelling air flows with the Navier-Stokes equations. With
this model, the effect of wind fields on smoke has already been investigated [FSJ01], and in this paper we
extend this approach to wind effects on textiles.
However, the solution of the sophisticated NavierStokes equations is not desired and not necessary in
all situations where wind effects shall be integrated
into cloth simulations. For this case, we present a
much simpler model based on tracing wind particles
that move along a global force field. During the simulation, the wind field is evaluated for each wind particle at its current position. The so determined flow
field is used to compute the wind force which is added
to the forces that act on the textiles. By detecting collisions between the wind particles and objects in the
scene, we are able to simulate the important effect of
lee even with this straightforward method.
Of course, both approaches have different characteristics and aim at different applications for wind simulation. In this work, we compare the models’ advantages and disadvantages and show practical results of
the described methods.
The rest of this paper is organized as follows. After giving an overview of related work in section 2,
we describe the aerodynamic force model applied in
this work in section 3. In section 4 we discuss the
two wind field models, namely the one based on the
Navier-Stokes equations in 4.1, and the one based on
tracing wind particles in 4.2. Finally, we show some
practical results of the implemented algorithms in section 5, before we conclude the paper in section 6.
2. PREVIOUS WORK
Models for fluid dynamics can be essentially subdivided into two categories. Simple models which are
commonly used in most computer graphics applications describe the wind flow by predefined flow functions. Here, global functions are defined to model the
velocity of wind. Either special flow primitives can be
combined [WH91; LDG96; Li00] or visually pleasing functions introducing random turbulence [SF92;
SF93; Sta97] are taken into account to model even
complex wind scenes. Many models use this method
to move objects in the wind field through the scene
[Ree83; Sim90; WH91; BLM95]. In addition, physically based fluid dynamics solving equations of motions with particle methods were presented recently
[IK03].
However, fixed flow functions lack interaction with
the user or objects in the scene. Hence, with increasing
computer power, computer graphics concentrates on
physically more accurate simulations. In many fields
the Navier-Stokes equations are the standard mathematical formulation to model fluid dynamics. A vast
literature exists on how to solve these equations numerically. CFD are applied in this field for engineering tasks with a high degree of quality requirements.
Unfortunately, it is quite difficult to apply these algorithms in computer graphics due to enormous calculation times. Hence, faster fluid solvers were investigated for computer graphics applications. Kajiya
et al. [KvH84], Yaeger et al. [YU86], and Gamito
et al. [GLG95] worked on fluid dynamics solvers in
two dimensions, and many improvements and variants
followed [CdVLHM97; KM90]. Foster and Metaxas
[FM96; FM97], and Griebel et al. [GDN98] presented
a solver for the fully three dimensional Navier-Stokes
equations. Due to explicit integration methods very
small step sizes had to be used. To enable faster
simulations, a solution with an unconditionally stable solver was introduced by Stam [Sta99] and further extended in [FSJ01; Sta01; Sta03]. Modelling
interaction of fluids with solid objects has been investigated by Takahashi et al. [TFK + 03] and Génevaux
et al. [GHD03]. Recently, Wei et al. [WZF + 03] presented an interesting approach to simulate lightweight
objects like soap bubbles and feathers in a wind flow
using a Lattice Boltzmann Model extended with a subgrid model.
For interaction of highly deformable objects and especially cloth-like objects only few models have been
investigated. Simple models consist in the calculation
of lift and drag forces from the surrounding velocity
field [SF92; Pro95; KCC+ 00; KCCL01]. More complex interaction models calculate the wind force by a
panel method [LDG96; Li00] introducing local vortices.
In this work, we show how recent results in fluid
dynamics for computer graphics can be exploited to
simulate interaction of wind flows with textiles. Moreover, we extend the more straightforward approach of
global wind field functions by the effect of lee.
3. AERODYNAMICS
To incorporate wind effects in a physically based animation we have to apply additional external forces
in the dynamical model of the deformable objects.
Hence, given a wind flow represented by a velocity
field in the scene we calculate the forces which are
exerted on the simulated objects. In this section, we
briefly describe the model we use to compute the effective aerodynamic forces such as wind force and air
resistance, mainly following [SF92].
The wind force acting on objects in an air stream is
decomposed into two components: the lift force F L
and the drag force F D (see figure 1).
cloth
wind direction
u
Vrel
FL
q
FD
^
n
Figure 1: The decomposition of wind forces (side
view).
The direction of the drag force F D is diametral to
the relative velocity v rel = vobject − u, where vobject
is the object’s velocity and u is the velocity field of the
wind. Note that in the case of a windless situation, i.e.
u = 0, we still have air resistance for moving objects.
Since two-dimensional objects do not exhibit an inside
and outside, the unit normal n̂i of the i-th face of the
object mesh (cf. figure 1) is replaced by
n̂i
if ni · vi,rel > 0 ,
ñi =
(3.1)
−n̂i else .
The drag force per face is then given by
Fi,D =
1
CD ρ|vi,rel |2 A · (ñi · v̂i,rel ) · (−v̂i,rel ) ,
2
where CD is the specific air resistance coefficient, ρ
the density of air, A is the area of the corresponding
face, and v̂i,rel the unit relative velocity vector of the
face.
The direction of the lift force, which is perpendicular to vi,rel and lies in the plane spanned by v i,rel and
ñi , is given by
ûi = (ñi × v̂i,rel ) × v̂i,rel .
Then the lift force is calculated as
Fi,L =
4.1.1 The solution of the Navier-Stokes equations
1
CL ρ|vi,rel |2 A cos θ · ûi ,
2
where CL is the lift force coefficient, and θ is the angle
between vi,rel and the actual face.
4. WIND FIELD MODELS
In this section we describe two different wind field
models and show how they can be used to model wind
effects on textiles. The first model is based on the work
of Stam [Sta97] and calculates the numerical solution
of the Navier-Stokes equation with a semi-Lagrangian
approach. This model is extended to interaction of the
wind flow with textiles. The second model employs
precomputed wind flows and particle tracing methods.
This approach is much easier to implement and can
be added to existing simulation modules without additional computational cost. In section 4.2, we show
how to produce realistic effects of wind on textiles including lee effects.
4.1 The Navier-Stokes equations
The Navier-Stokes equations describe a precise mathematical model for fluid flows. The numerical algorithms used in CFD to solve these equations are designed for physical accuracy for engineering applications and are expensive in computation. But in our
case where this precision is not necessary simplifications can be made which greatly reduce the computation costs as described by Stam [Sta03]. Since
the arising wind velocities are clearly below the speed
of sound, compressibility effects are negligible, and
the wind is modelled as an incompressible constant
density fluid. This notably simplifies the numerical
approximation, and the incompressible Navier-Stokes
equations can be written in a compact vector notation
as
∇ · u = 0,
(4.1)
1
∂u
= −(u · ∇)u − ∇p + ν∇2 u + f .
∂t
ρ
for external forces. The first equation states that the
velocity field should be incompressible while the second one describes the evolution of a velocity field over
time. The first term on the right hand side reflects the
change of velocity due to advection, while the second
expression accounts for any external force f and acceleration caused by the local pressure gradient ∇p and
by viscous drag depending on ν.
(4.2)
Here, u describes the (three-dimensional) velocity
field, ν is the kinematic viscosity of the fluid, ρ its density, p the pressure in the wind field, and f accounts
In the following we briefly describe the numerical solution of the Navier-Stokes equations (4.1) and (4.2)
by Stam [Sta97]. To solve these equations numerically they first have to be discretised. For this, the
computational domain is diced up into equally sized
cubes forming a grid as described in section 4.2.2, and
sample values of velocity and pressure are defined at
the cell centres. Foster and Metaxas [FM96] use a
finite difference approximation for the discretisation
of the operators in equation (4.2). Then they update
the cell’s velocities according to the divergence value
computed in each direction, respectively, using an explicit integration scheme. Since time steps in explicit
computations usually need to be very small, we follow Stam [Sta99] who proposes an implicit integration
scheme, which allows stable simulations with large
time steps. While the linear terms in equation (4.2) are
straightforward to solve implicitly, the term −(u · ∇)u
is nonlinear and deserves special attention. Here, a different approach based on the method of characteristics
is used to solve the advection equation. Equation (4.2)
does not provide a divergent-free velocity field. Therefore, the divergence of each cell in the grid has to be
projected to zero using the Helmholtz-Hodge decomposition [Sta03].
4.1.2 Wind effects on clothes
The major advantage of Navier-Stokes based approaches consists in the fact that the evolution of
the wind flow over time is calculated. It enables us
to model global effects like convection and diffusion
on a physical basis. We present a model to exploit
these wind models for calculating the interaction of
deformable objects with the air flow by a boundary
condition method.
As already stated by Stam [Sta03] “a velocity field
of its own isn’t really visually interesting until it starts
moving objects [...]”. That means in particular that all
objects in the scene interact with the fluid present in
it, i.e. in our case clothes with the wind. On the one
hand the wind deforms the objects which on the other
hand change the wind flow. To describe the above situation by a physical model we require the Neumann
boundary condition
∂u
=0
∂n
to be satisfied for the wind flow u at any boundary
point of an object with normal n. Rigid objects like
walls will influence the fluid field but will not be affected by fluid forces themselves. Deformable objects
like cloth are supposed to both experience fluid forces
and itself influence the fluid flow. This in fact is a
major difficulty. Consider a point p b on the boundary of a deformable object in the scene. Let u(p b )
be the corresponding wind velocity at that point and
n be its normal. On the one hand, we want the Neumann boundary condition u(p b ) · n = 0 to be satisfied. On the other hand, the wind velocity orthogonal to the object’s surface is just what causes the aerodynamic forces. Without further remedial action setting the boundary according to the Neumann condition
would mean that the fluid will not exert forces on the
objects.
Here we propose a method which meets both requirements. For every deformable object the velocity
value of the surrounding wind field for every vertex of
the representing mesh is tracked. In the solver’s cycle,
the boundary conditions are then set prior to any other
operation: For every object in the scene each triangle
of its representing mesh is registered in the fluid grid,
which means that the cell of the wind field occupied
by the object is marked as occupied. The wind velocity at the vertex positions of the object is recorded.
Additionally, the normals of these vertices are stored.
Then, the aerodynamic forces as described in section
3 are calculated. Finally, for every marked cell in the
scene the previously stored normals are averaged in
one space cell which are used to update the velocity
at the cell to satisfy the Neumann boundary condition.
Thus, the boundary conditions are met and yet aerodynamic forces are obtained.
A different issue is how to deal with the inside of
(rigid) objects. The method to set boundary conditions
as described above does not account for the interior of
objects. Thus, a nonzero velocity could be mistakenly
assigned to cells lying inside an object. To avoid this
situation, the path of the wind flow is checked for object intersection, whereby the collision detection of the
cloth simulation system provides a simple method to
deal with this issue [MKE03].
4.2 Particle Tracing on Wind Fields
Here we combine the idea of creating wind fields
by predefined flow primitives with particle tracing in
given flow fields. To define a wind scene we first built
up the air flow by simple primitives such as parallel
directed wind fields, vortices, etc. We then use a par-
ticle tracing method in the defined wind field to determine the effect of lee by detecting windless areas.
This method is very easy to implement and yields very
plausible and nicely looking results.
4.2.1 Global Wind Fields
A simple approach to generate complex air flows is to
define a wind field by mathematical functions which
assign to each point in space a unique velocity value.
As Wejchert et al. [WH91] have shown, this already
enables an animator to design even complex wind
fields: Assuming an irrotational (∇ × u = 0), inviscid, and incompressible (∇ · u = 0) fluid, the NavierStokes equations which describe the mechanics of any
fluid (see section 4.1) can be simplified to give the
Laplace equation
∇ · u = ∇∇φ = ∇2 φ = 0,
(4.3)
where φ is the potential of the given wind field. Thus,
the velocity field u is given by
u = ∇φ .
The linearity of equation (4.3) enables an animator to
combine basic flows which satisfy equation (4.3) as
he likes and thus to obtain complex fluid flows. Some
primitives common to fluid simulations are depicted in
figure 2.
Directional
Vortex
Point
Figure 2: Flow primitives
One drawback of this model is that it cannot handle objects exhibiting complex boundaries. The approach to model solid objects in the scene taken by
Wejchert et al. consists in placing a wind source using
a mirror principle in order to extinguish the air flow
at the boundary of the object. While this works for
simple objects this approach is not feasible at all with
deformable objects like textiles.
Another more serious drawback of this model for
our application consists in the lack of interaction with
objects. The wind flow defined by the primitives will
not react on objects in the scene which means for example that tissues in the lee of other objects will be
affected by the wind flow as well.
However, this method can be combined with the
aerodynamic model described in section 3 to give nice
and fast results as will be shown in section 5. To solve
the described problems we propose a model which
combines the simple global wind flow techniques with
a particle tracing method. Here, particles are moved
along the wind field to determine the effect of objects
in the scene.
4.2.2 Particle Tracing
This model divides the scene into parallelepiped cells.
There are two common approaches to discretising the
continuous velocity field defined in space: one can either choose the midpoint of a cell [Sta99] or its six
faces [FM96] to define the field. As usual, values between the defining points of the grid are interpolated
using trilinear functions.
The basic idea of the particle tracing method
is to
trace wind particles through a field w =
i wi defined by linear superposition of wind sources corresponding to flow primitives with respective velocity
fields wi . The field w does not account for lee effects caused by objects in the flow. Therefore we compute the wind field u containing these effects as follows. In our model every wind source is also a particle source: These particles form an uncoupled particle
system which can be considered as a wind gust. The
wind particles are emitted into the velocity field w i of
the corresponding wind source which is defined on a
grid. The specific emission intervals and amounts depend on the properties of the flow sources.
In every time step each particle in a wind gust moves
along its velocity field w i defined by the corresponding wind source. Notice that the movement of the particles in a wind gust is only affected by the wind source
they belong to. The global superposition of all wind
sources has no effect on these particles. To calculate
the wind particles’ positions we used the explicit Euler
integration scheme. For a wind particle at position p t
and time t this results in a path s(p t , pt+∆t ), where
pt+∆t denotes the position after time step ∆t according to
pt+∆t = pt + wi (pt , ∆t) .
As a particle moves along its path in space, all grid
cells colliding with the path are updated with the velocity of the associated wind source with respect to the
position of the particle. The particle might cross several grid cells on its way during a single time step. If
this is the case, the path of the particle has to be subdivided into parts not exceeding the size of a grid cell.
This path is then tested for collisions with the objects
in the scene. The velocity field u is then computed as
u=
wi
for each grid cell separately, where w i are all those
wind sources whose particles have reached the cell.
If a collision is detected at position p col the normal
of the colliding object n obj (pcol ) is determined and
the velocity of the particle is set to
wi (pcol , t+∆t) = wi (pcol , t)−(nobj ·wi (pcol , t))·nobj .
This assures that the velocity component of the resulting field u is orthogonal to the collision object’s surface at pcol is zero, i.e.
u(pcol , t + ∆t) · nobj = 0 ,
and thus no flow propagates through the object.
The wind force effective on objects in the scene is
then computed from the velocity field u. Since u is determined using the wind particles, every point p that
could not be reached by any wind particle will hold
zero velocity even if w may hold a nonzero velocity. Thus, this method solves the problems described
in section 4.2.1.
Note that the somewhat tempting simplification of
tagging each cell to either have wind in it or not is
not valid. Imagine the simple scene in which there are
two directional wind sources with opposite wind directions. Let them further have equal velocity magnitude
and no distance attenuation. If we now place a solid
object in between these two sources a rather undesired
effect would occur using this simplification: on both
sides of the solid object all cells would be tagged as
having wind. But evaluating the wind field at every
cell we would obtain a zero velocity. This is due to
the extinguishing effect of the superposition of the two
wind sources. Therefore, it is crucial for the particles
to have the associated velocity of their wind source and
not just the velocity resulting from the global superposition of all wind sources.
4.3 Comparison
In this section we comment on the different models
described in this paper. For physically accurate simulations based on the common method in fluid dynamics the model introduced by Stam produces realistic effects which global wind field models can never
achieve. It produces nice swirls and vortices derived
from dynamical characteristics of the fluid. However
implementing the fluid solver is quite complex and using a high grid resolution is computationally expensive. Hence, the global wind field model is better
suited for an easy to implement tool which is easy to
adapt to specific situations. Particle systems are very
common in the simulation engines and most functionality can be adapted to integrate the proposed wind
model. Even with this straightforward approach, nice,
realistic looking results can be achieved which is illustrated in the next section.
5. RESULTS
7. Acknowledgements
In this section we present some practical results of the
previously described methods. We implemented the
wind models described in sections 4.1 and 4.2 in a
cloth animation system that employs a fast finite element method to simulate the drape of textiles with
measured material properties [EKS03]. For collision
detection (between deformable objects, rigid objects,
and wind particles) we use k-DOP hierarchies as described in [MKE03].
Figure 3 shows a flag blowing in the wind. We used
the particle tracing method described in section 4.2 to
model the effects of a directional wind field on the flag.
In figures 4 and 5 we show the ability of both the
Navier-Stokes equations model (section 4.1) and the
particle tracing method (section 4.2) to model the effect of lee. Two flags are exposed to a wind field, but
the wind is blocked by a wall, so one of the flags is not
affected by the wind.
The images in figure 6 show a character wearing a
shirt and standing in a wind stream coming from the
front. Images (a) and (b) are snapshots from the beginning of the animation, images (c) and (d) show the
result after the wind field has affected the clothes. To
show the improved realism when simulating lee effects, we let the the wind act on all polygons of the
shirt on the right (no lee effect). For the shirt on the
left we used the Particle Tracing Method to simulate
lee effects which, we think, gives more realistic results
(see also the accompanying video).
This work was partially supported
bmb+f
research
project
Virtual
(www.VirtualTryOn.de).
6. CONCLUSIONS
We presented two models for including advanced wind
effects into cloth simulation systems. The first concentrates on physically accurate computations using a
semi-Lagrangian approach to solve the Navier-Stokes
equations, the second model incorporates a particle
tracing method for global wind fields. As illustrated
in the previous section both methods produce realistic
looking results which are capable of enhancing the realism of computer animations. While the first model
has a wider range of applications, the second one provides an easy method which still delivers realistic effects such as air resistance and lee.
All methods described in this work should be easy
to extend to three-dimensional deformable objects. All
the methods apply the same except for simple changes.
Since three-dimensional objects define an inner and
outer part, the adaption of the face normals in equation (3.1) is not necessary. Moreover, in the wind field
computation care has to be taken that no wind field is
present in the object. Here, the same method as described for rigid objects (section 4.2.2) can be applied.
by the
Try-On
8. References
[BLM95] B. Becker, D.A. Lane, and N. Max. Unsteady Flow Volumes. In Proc. of Visualization,
1995.
[BTH+ 03] K. S. Bath, C. D. Twigg, J. K. Hodgins,
P. K. Khosla, Z. Popovic, and S. M. Seitz. Estimating Cloth Simulation Paramters from Video. In
Proc. SIGGRAPH Symposium on Computer Animation, 2003.
[CdVLHM97] J.X. Chen, N. da Vittorio Lobo, C.E.
Hugues, and J.M. Moshell. Real-Time Fluid Simulation in a dynamic Virtual Environment. IEEE
Computer Graphics and Applications, pages 52–
61, 1997.
[EKS03] Olaf Etzmuß, Michael Keckeisen, and
Wolfgang Straßer. A Fast Finite Element Solution
for Cloth Modelling. Proc. Pacific Graphics, 2003.
[FM96] Nick Foster and Dimitri Metaxas. Realistic
animation of liquids. Graphical models and image
processing: GMIP, 58(5):471–483, 1996.
[FM97] Nick Foster and Dimitri Metaxas. Modeling the Motion of a Hot, Turbulent Gas. In Proc.
SIGGRAPH Symposium on Computer Animation,
pages 181–188, 1997.
[FSJ01] Ronald Fedkiw, Jos Stam, and Henrik Wann
Jensen. Visual simulation of smoke. In Computer
Graphics (Proc. SIGGRAPH), pages 15–22, 2001.
[GDN98] M. Griebel, T. Dornseifer, and T. Neunhoeffer. Numerical Simulation in Fluid Dynamics: A
Practical Introduction. SIAM, Philadelphia, 1998.
[GHD03] O. Génevaux, A. Habibi, and J.-M. Dischler. Simulating Fluid-Solid Interaction. In
Graphics Interface, pages 31–38, 2003.
[GLG95] M.N. Gamito, P.F. Lopez, and M.R.
Gomes. Two-dimensional Simulaton of Gaseous
Phaenonemna Using Vortex Particles. In Proc. of
the 6th Eurographics Workshop on Computer Animation and Simulation, pages 3–15, 1995.
[IK03] T. Ilmonen and J. Kontkanen. The Second
Order Particle System. Journal of WSCG, 11(1),
2003.
[KCC+ 00] Young-Min Kang, Jeong-Hyeon Choi,
Hwan-Gue Cho, Do-Hoon Lee, and Chan-Jong
Park. Real-time Animation Technique for Flexible and Thin Objects. In Journal of WSCG, pages
322–329, 2000.
[KCCL01] Y.-M. Kang, J.-H. Choi, H.-G. Cho, and
D.-H. Lee. An efficient animation of wrinkled
cloth with approximate implicit integration. The
Visual Computer, 17(3), 2001.
[TFK+ 03] T. Takahashi, H. Fuijii, A. Kunimatsu,
K. Hiwada, T. Saito, K. Tanaka, and H. Ueki. Realistic Animation of Fluid with Splash and Foam.
Computer Graphics Forum, 22(3):391–400, 2003.
[KM90] M. Kass and G. Miller. Rapid, Stable
Fluid dynamics for Computer Graphics. In Proc.
SIGGRAPH Symposium on Computer Animation,
pages 49–57, 1990.
[WH91] J. Wejchert and D. Haumann. Animation
aerodynamics. Computer Graphics (Proc. SIGGRAPH), 25(2):19–22, July 1991.
[KvH84] J.T. Kajiya and B.P. von Herzen. Ray Tracing Volume Densities. In Proc. SIGGRAPH Symposium on Computer Animation, pages 165–174,
1984.
[LDG96] L. Li, M. Damoran, and R. K. Gay. Aerodynamic force models for animating cloth motion
in air flow. The Visual Computer, 12, 1996.
[Li00] L. Li. Cloth Modeling and Animation, chapter
Aerodynamic Effects, pages 175–195. A.K. Peters,
2000.
[MKE03] Johannes Mezger, Stefan Kimmerle, and
Olaf Etzmuß. Hierarchical Techniques in Collision
Detection for Cloth Animation. Journal of WSCG,
11(2):322–329, 2003.
[Pro95] Xavier Provot. Deformation Constraints in
a Mass-Spring Model to Describe Rigid Cloth Behavior. In Graphics Interface ’95, pages 147–154,
1995.
[Ree83] W. T. Reeves. Particle Systems — A Technique for Modeling a Class of Fuzzy Objects.
In Computer Graphics (Proc. SIGGRAPH), pages
359–376, 1983.
[SF92] M. Shinya and A. Fournier. Stochastic Motion: Motion under the Influence of Wind. Computer Graphics Forum, 58(5):119–128, 1992.
[SF93] Jos Stam and Eugene Fiume. Turbulent Wind
Fields for Gaseous Phenomena. Computer Graphics (Proc. SIGGRAPH), pages 369–376, 1993.
[Sim90] Karl Sims. Particle animation and rendering using data parallel computation. In Computer Graphics (Proc. SIGGRAPH), pages 405–
413, 1990.
[Sta97] Jos Stam. A General Animation Framework
for Gaseous Phenomena. ERCIM Research Report
R047, 1997.
[Sta99] J. Stam. Stable fluids. Computer Graphics
(Proc. SIGGRAPH), pages 121–128, 1999.
[Sta01] Jos Stam. A simple fluid solver based on the
FFT. Journal of Graphics Tools: JGT, 6(2):43–52,
2001.
[Sta03] J. Stam. Real-time fluid dynamics for games.
Proceedings of the Game Developer Conference,
March 2003.
[WZF+ 03] Xiaoming Wei, Ye Zhao, Zhe Fan, Wei
Li, Suzanne Yoakum-Stover, and Arie Kaufman.
Blowing in the wind. In Proc. of SIGGRAPH Symposium on Computer Animation 2003, pages 75–
85. Eurographics Association, 2003.
[YU86] L. Yaeger and C. Upson. Combining Physical and Visual Simulation. Creation of the Planet
Jupiter for the Film 2010. In Proc. SIGGRAPH
Symposium on Computer Animation, pages 85–93,
1986.
Figure 3: Flag blowing in the wind (particle tracing method).
Figure 4: Two flags blowing in the wind (Navier-Stokes equations). The wind is blocked by the wall, so the right
flag is in the lee. Note that the simulation starts with both flags in an unfolded state.
Figure 5: Two flags blowing in the wind (particle tracing method). The wind is blocked by the wall, so the right
flag is in the lee (compare figure 4).
(a)
(b)
(c)
(d)
Figure 6: A character wearing a shirt and standing in a wind stream coming from the front. Images (a) and (b) are
snapshots from the beginning of the animation, images (c) and (d) show the result after the wind field has affected
the clothes. To show the improved realism when simulating lee effects, we let the the wind act on all polygons of
the shirt on the right (no lee effect). For the shirt on the left we used the particle tracing method to simulate lee
effects which gives more realistic results.